Core and slice the cabbage into 1⁄2-in ribbons (you want about 4 cups total) and place in a large salad bowl.
In a jar with a lid, vigorously shake together the olive oil, lemon and lime juices, lemon zest, garlic, shallot, egg yolk, and mustard, until emulsified.
Toss 3⁄4 of the dressing and the salt with the cabbage until all leaves are well coated. Sprinkle parsley and cilantro leaves over cabbage.
Cut the radishes into paper-thin slices with a mandoline or a very sharp knife. Arrange the radish slices over most of the top of the cabbage salad. Spoon over or brush olive oil directly onto the radishes.
MAKE AHEAD: This salad can be made up to an hour ahead of time, and is excellent the next day.